The next generation Internet is designed to accommodate flows that span across multiple domains with quality of service guarantees, in particular bandwidth. In this context, destinations for inter-domain traffic may be reachable through multiple egress routers within a domain. In this paper, we formulate a bandwidth guaranteed egress router selection problem. The objective is to, for each aggregated inter-domain traffic flow, select an egress router that satisfies the end-to-end bandwidth requirement while optimizing the network resource utilization by which we consider three objective functions: minimizing the total bandwidth consumption, improving intra-domain and inter-domain load balancing in the network. We propose a heuristic algorithm with five egress router selection policies to solve this problem. The evaluation of these egress router selection policies through simulation benefits ISPs by choosing the one that fits their target objectives.